Problem: Solve for $x$ and $y$ using substitution. ${6x+2y = -6}$ ${y = 3x+9}$
Solution: Since $y$ has already been solved for, substitute $3x+9$ for $y$ in the first equation. ${6x + 2}{(3x+9)}{= -6}$ Simplify and solve for $x$ $6x+6x + 18 = -6$ $12x+18 = -6$ $12x+18{-18} = -6{-18}$ $12x = -24$ $\dfrac{12x}{{12}} = \dfrac{-24}{{12}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = 3x+9}\thinspace$ to find $y$ ${y = 3}{(-2)}{ + 9}$ $y = -6 + 9$ $y = 3$ You can also plug ${x = -2}$ into $\thinspace {6x+2y = -6}\thinspace$ and get the same answer for $y$ : ${6}{(-2)}{ + 2y = -6}$ ${y = 3}$